NTRU is one of the most widely used public-key cryptosystems and its security has been an active research topic. This paper proposes a new way to find NTRU-2005 private key. The algorithm is based on meet-in-the-middle attack and a quantum algorithm for searching the fixed weight target. Compared with the current classical and quantum meet-in-the-middle attacks, our algorithm has lower time and space complexity. Moreover, this attack can also be applied against different versions of NTRU. The result can help to understand the security of NTRU better. quantum algorithm, NTRU, meet-in-the-middle attack Citation:Wang H, Ma Z, Ma C G. An efficient quantum meet-in-the-middle attack against NTRU-2005. Chin Sci Bull, 2013, 58: 35143518, doi: 10.1007 For all the time, how to use the quantum computational theory to improve the classical cryptanalysis ability is an important issue. NTRU is a public-key cryptosystem based on the shortest lattice vector problem. At equivalent security level, NTRU needs lower memory and smaller computational complexity than RSA. Now, there is no efficient quantum algorithm known that will solve the shortest lattice vector problem. So, it is believed that NTRU is secure in quantum times [1]. In fact, with the rapid development of quantum computation, all cryptosystems based on the problems of large integer factorization and discrete logarithm are potentially fragile. However, it is still unclear what kind of effects the quantum computational theory could make on the security of NTRU till now. Classical meet-in-the-middle (MITM) attack is a generic cryptanalytic method originally developed from cryptanalysis of block ciphers. Recently, this technique is also found to be quite useful in the cryptanalysis of public-key cryptography. MITM attack is the best algorithm for attacking NTRU at present. Grover [2] proposed a generic quantum search algorithm which gives a quadratic speedup over the classical brute-force search. However, it is not yet known whether Grover algorithm can speed up the classical MITM attack.There are some new developments in the classical cryptanalysis of NTRU, such as lattice attack, hybrid attack [3], broadcast attack [4], etc. Ludwig [5] combined lattice reduction technique with Grover algorithm, and put forward a novel quantum attack algorithm against NTRU. However, the attack algorithm in [5] is not better than classical MITM attack. In 2011, a quantum algorithm used to find fixed weight target was proposed [6]. At the same time, the author analyzed the security of NTRU by the proposed algorithm. The computation complexity of Wang's algorithm is significantly lower than a classical brute-force search, but still higher than a classical MITM attack.Xiong et al. [7] combined MITM attack with Grover quantum searching algorithm, and developed a quantum MITM attack method against NTRU. The time complexity

In order to address the scenario in which the user wants to access the real-time data directly from the sensor node in wireless sensor networks (WSNs), Das proposed a two-factor authentication scheme. In 2010, Khan et al. pointed out that Das's scheme has some security flaws and proposed an improved scheme. Recently, Yuan demonstrated that Khan et al.'s improvement is still insure against several attacks. Yuan also proposed an enhanced two-factor user authentication scheme using user's biometrics to fix the security flaws in Khan et al.'s scheme. In this paper, we show that Yuan's scheme still suffers from the stolen smart card attack and the GW-node impersonation attack. Moreover, biometric keys are misused in Yuan's scheme such that even the valid user cannot pass the biometric verification. To remedy these problems, we propose an improved two-factor authenticated key distribution scheme based on fuzzy extractors. Security and performance analysis demonstrates that our scheme is more secure and efficient than previous schemes.

Secure and efficient authentication protocols are necessary for cloud service. Multifactor authentication protocols taking advantage of smart card, user’s password, and biometric, are more secure than password-based single-factor authentication protocols which are widely used in practice. However, most of the multiserver authentication protocols may have weak points, such as smart card loss attack, man-in-the-middle attack, anonymity, and high computation cost of authentication center. In order to overcome the above weaknesses, we propose a novel multiserver multifactor authentication protocol based on the Kerberos protocol using the extended Chebyshev chaotic mapping as a cryptographic algorithm. The proposed protocol achieves anonymity without sharing secret keys in advance and needs the user to register with the authentication center only once. Finally, we prove the security of the new protocol with BAN logic and compare it with other multifactor authentication protocols for multiserver environment. The results show that our proposed protocol is more secure and efficient and better for practical application.

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